If first term \(u_{1}\)and last term \(u_{n}\) of an arithmetic series is given then the sum if the series is \(S_{ n }=\frac { n }{ 2 } [u_{ 1 }+u_{ n }]\)

That is Sum up to infinity in arithmetic sequence is infinite only, so sum up to infinity is not possible in arithmetic sequence.

II. Geometric Sequence and Series

Geometric sequence is a sequence of numbers such that the ratio or division of two consecutive terms is constant. For example, the sequence 2, 6, 12, 24, 48, 96, . . . is a geometric sequence with common ratio of 3.

In a geometric sequence , First term is \(u_{1}\) , Common ratio is \(r\) , General term of a sequence \(u_{n}\), Sum of first n terms \(S_{n}\)